A193981 Number of ways to arrange 3 nonattacking triangular rooks on an nXnXn triangular grid

0, 0, 0, 2, 23, 127, 468, 1352, 3310, 7190, 14260, 26330, 45885, 76237, 121688, 187712, 281148, 410412, 585720, 819330, 1125795, 1522235, 2028620, 2668072, 3467178, 4456322, 5670028, 7147322, 8932105, 11073545, 13626480, 16651840, 20217080

Offset

1,4

Comments

Column 3 of A193986

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Christopher R. H. Hanusa, Thomas Zaslavsky, A q-queens problem. VII. Combinatorial types of nonattacking chess riders, arXiv:1906.08981 [math.CO], 2019.

Formula

Empirical: a(n) = 6*a(n-1) -14*a(n-2) +14*a(n-3) -14*a(n-5) +14*a(n-6) -6*a(n-7) +a(n-8)

Contribution from Vaclav Kotesovec, Aug 31 2012: (Start)

Empirical: G.f.: -x^4*(2 + 11*x + 17*x^2)/((-1+x)^7*(1+x))

Empirical: a(n) = 13*n/24 - 11*n^2/24 - 23*n^3/48 + 9*n^4/16 - 3*n^5/16 + n^6/48 + 1/4*floor(n/2)

(End)

Example

Some solutions for 5X5X5
......0..........0..........0..........0..........0..........0..........0
.....0.0........0.0........0.0........0.0........0.1........0.0........0.1
....0.0.1......1.0.0......0.1.0......0.1.0......0.0.0......0.1.0......1.0.0
...0.1.0.0....0.0.0.1....1.0.0.0....0.0.0.1....1.0.0.0....1.0.0.0....0.0.0.0
..1.0.0.0.0..0.1.0.0.0..0.0.1.0.0..0.0.1.0.0..0.0.1.0.0..0.0.0.0.1..0.0.0.1.0

Crossrefs

Sequence in context: A041579 A185830 A301665 * A235594 A053299 A356828

Adjacent sequences: A193978 A193979 A193980 * A193982 A193983 A193984

Keyword

nonn

Author

R. H. Hardin Aug 10 2011

Status

approved